The present invention relates to a row of blades for use in a turbo-machine. More specifically, the present invention relates to a row of blades having resonant frequencies that are mix-tuned so as to inhibit stall flutter vibration.
The flow path of an axial flow turbomachine, such as a steam turbine, is formed by a stationary cylinder and a rotor. A large number of stationary vanes are attached to the cylinder in a circumferential array and extend inward into the steam flow path. Similarly, a large number of rotating blades are attached to the rotor in a circumferential array and extend outward into the steam flow path. The stationary vanes and rotating blades are arranged in alternating rows so that a row of vanes and the immediately downstream row of blades form a stage. The vanes serve to direct the flow of steam so that it enters the downstream row of blades at the correct angle. The blade airfoils extract energy from the steam, thereby developing the power necessary to drive the rotor and the load attached to it.
The amount of energy extracted by each row of rotating blades depends on many factors, including the size and shape of the blade airfoils, as well as the quantity of blades in the row. Thus, the shapes of the blade airfoils are an extremely important factor in the thermodynamic performance of the turbine and determining the geometry of the blade airfoils is a vital portion of the turbine design.
As the steam flows through the turbine its pressure drops through each succeeding stage until the desired discharge pressure is achieved. Thus, the steam properties--that is, temperature, pressure, velocity and moisture content--vary from row to row as the steam expands through the flow path. Consequently, each blade row employs blades having an airfoil shape that is optimized for the steam conditions associated with that row.
Designing a steam turbine blade is made difficult by the fact that the airfoil shape determines, in large part, the mechanical strength of the blade and its resonant frequencies, as well as the thermodynamic performance of the blade. These considerations impose constraints on the choice of blade airfoil shape so that, of necessity, the optimum blade airfoil shape for a given row is a matter of compromise between its mechanical and aerodynamic properties.
During operation of a the turbine, the rotating blades are subject to forced vibration due to oscillatory excitation at frequencies which coincide with integer multiples, referred to as harmonics, of the rotor rotational frequency. Such excitation is referred to as synchronous excitation. Synchronous blade excitation can be created by non-uniformities in the flow of the motive fluid (i.e., steam in the case of a steam turbine) that may vary in space around the circumference of the turbine. Such non-uniformities result from the presence of such features as extraction pipes and reinforcing ribs, as well as imperfections in the shape and spacing of the stationary vanes.
As a result of the oscillatory excitation, turbine blades undergo high frequency deflections that create vibratory stresses in the blades. These vibratory stresses can result in high cycle fatigue cracking if their magnitude is not controlled. This problem is exacerbated by the fact that a turbine blade typically has a number of resonant frequencies associated with its various vibratory modes--i.e., tangential bending, axial bending, torsional, etc. If the frequency of the oscillatory excitation to which the blade is subjected is close to one of its resonant frequencies, the vibratory stresses can quickly build up to destructive levels. To avoid this occurrence, in turbines with rotors that are intended to operate at, or very near to, a single rotational frequency, the rotating blades are typically designed so that at least one, and preferably as many as possible, of the lower resonant frequencies do not coincide with harmonics of the rotor rotational frequency--typically referred to as "tuning." Traditionally, within a given row the blade airfoil shapes are identical, so that all of the blades are similarly tuned.
In contrast to forced vibration, a complex aerodynamic phenomenon known as stall flutter may occur even if the blades are properly tuned between two harmonics. Briefly, stall flutter is an aero-elastic instability wherein, under certain flow conditions, vibratory deflections in the airfoil cause changes in the aerodynamic loading on it that tend to increase, rather than dampen, the deflections. Consequently, stall flutter can increase the vibratory stress on the blade and cause high cycle fatigue cracking. Stall flutter may occur when two or more adjacent blades in a row vibrate at a frequency close to their natural resonant frequency for the first mode of vibration (i.e., tangential bending) and the vibratory motion between the two blades assumes a certain phase relationship.
One solution proposed in the past for increasing the resistance of the blade row to stall flutter is to form the row using blades of varying frequency--a method referred to as "mix-tuning." The mix-tuned blades are installed in the row so that each blade alternates with another blade having a slightly different resonant frequency. Such mix-tuning makes it more difficult for the blades to vibrate at the same frequency, thereby inhibiting stall flutter.
One method of achieving such mix-tuning involves profiling the tips of half of the blades in the row in order to modify their resonant frequency, as discussed in U.S. Pat. No. 4,878,810 (Evans), hereby incorporated by reference in its entirety. Unfortunately, such tip profiling increases manufacturing cycle time and is detrimental to thermodynamic performance.
It is therefore desirable to provide an alternate method for mix-tuning the blades in a turbomachine.